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lfunc_lfunctions • Show schema
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{'Lhash': '1735145720341837867116346774732', 'a10': [0.5557234720776075, -0.9625412885970005], 'a2': [0.0, 1.3790549724002508], 'a3': [-1.4406015070335512, 2.495195003642404], 'a4': [0.0982073830981435, 0.0], 'a5': [-0.6979716602027064, -0.40297412590476256], 'a6': [-3.441011076881319, -1.9866686715219137], 'a7': [0.06998697422813796, -2.644825480714822], 'a8': [0.0, 2.893543324788413], 'a9': [-2.6506654041346778, -4.591087153826353], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.06998697422813796, 2.644825480714822]]], [13, [[1.0, 0], [2.365805103344664, -2.720839247913839]]]], 'bad_primes': [7, 13], 'central_character': '91.23', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '5185688524776875763118195925546', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.3790549724002508], [-2.0, 0]], [[1.0, 0], 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[[1.0, 0], [9.755719013265656, -16.897400995341833], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-91-91.23-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/91/2/k/b/23/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8366069748225475, 0.7653171452206504, 0.7039745253447175, 0.648153375483915, 0.5934979781090153, 0.5360136628045304, 0.47227326844010453, 0.39955117330743295, 0.31591654806480135, 0.2203140476147223, 0.11264667791907394, -0.006137888091414428, -0.13396583935167644, -0.26757444415493353, -0.40248434572191516, -0.5330237647909426, -0.652420265070796, -0.75297312943783, -0.8263153768090524, -0.8637690277452837, -0.8567904789795049, -0.7974949787374157, -0.6792405686865769, 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'7.84091803057780662220014657625292', '9.466148012820583884402947854063119', '11.04128601822039403791564013435899', '11.80248043684492892870384959267320', '12.19486738038132871429595125576441', '13.14999965882120202699708749665615'], 'prelabel': '2-91-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.779851151040083, 'root_number': '-0.770215084551955 - 0.6377842296016928*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38992557552', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36878862363922681752185491903', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10132776733547695672129432767', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.64850931975274013459026071637', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '91.23', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/k/b/23/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-91-91.23-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-91-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.3899255755200415, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36878862363922681752185491903', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1735145720341837867116346774732', 'Lhash_array': ['1735145720341837867116346774732'], 'label': '2-91-91.23-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/k/b/23/5'}